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<div class="titlepage"><div><div><h3 class="title">
<a name="boost_multiprecision.tut.floats"></a><a class="link" href="floats.html" title="Floating-point Types">Floating-point Types</a>
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<dt><span class="section"><a href="floats/cpp_bin_float.html">cpp_bin_float</a></span></dt>
<dt><span class="section"><a href="floats/cpp_dec_float.html">cpp_dec_float</a></span></dt>
<dt><span class="section"><a href="floats/gmp_float.html">gmp_float</a></span></dt>
<dt><span class="section"><a href="floats/mpfr_float.html">mpfr_float</a></span></dt>
<dt><span class="section"><a href="floats/float128.html">float128</a></span></dt>
<dt><span class="section"><a href="floats/fp_eg.html">Examples</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="floats/fp_eg/floatbuiltinctor.html">Construction
          from Specific Values Without Precision Loss</a></span></dt>
<dt><span class="section"><a href="floats/fp_eg/aos.html">Area of
          Circle</a></span></dt>
<dt><span class="section"><a href="floats/fp_eg/caveats.html">Drop-in
          Caveats</a></span></dt>
<dt><span class="section"><a href="floats/fp_eg/jel.html">Defining
          a Special Function.</a></span></dt>
<dt><span class="section"><a href="floats/fp_eg/nd.html">Calculating
          a Derivative</a></span></dt>
<dt><span class="section"><a href="floats/fp_eg/gi.html">Calculating
          an Integral</a></span></dt>
<dt><span class="section"><a href="floats/fp_eg/poly_eg.html">Polynomial
          Evaluation</a></span></dt>
<dt><span class="section"><a href="floats/fp_eg/variable_precision.html">Variable-Precision
          Newton Evaluation</a></span></dt>
<dt><span class="section"><a href="floats/fp_eg/gauss_lagerre_quadrature.html">Gauss-Laguerre
          quadrature</a></span></dt>
</dl></dd>
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<p>
        The following back-ends provide floating-point arithmetic:
      </p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend Type
                </p>
              </th>
<th>
                <p>
                  Header
                </p>
              </th>
<th>
                <p>
                  Radix
                </p>
              </th>
<th>
                <p>
                  Dependencies
                </p>
              </th>
<th>
                <p>
                  Pros
                </p>
              </th>
<th>
                <p>
                  Cons
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">cpp_bin_float</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;</span></code>
                </p>
              </td>
<td>
                <p>
                  boost/multiprecision/cpp_bin_float.hpp
                </p>
              </td>
<td>
                <p>
                  2
                </p>
              </td>
<td>
                <p>
                  None
                </p>
              </td>
<td>
                <p>
                  Header only, all C++ implementation. Boost licence.
                </p>
              </td>
<td>
                <p>
                  Approximately 2x slower than the <a href="http://www.mpfr.org" target="_top">MPFR</a>
                  or <a href="http://gmplib.org" target="_top">GMP</a> libraries.
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">cpp_dec_float</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;</span></code>
                </p>
              </td>
<td>
                <p>
                  boost/multiprecision/cpp_dec_float.hpp
                </p>
              </td>
<td>
                <p>
                  10
                </p>
              </td>
<td>
                <p>
                  None
                </p>
              </td>
<td>
                <p>
                  Header only, all C++ implementation. Boost licence.
                </p>
              </td>
<td>
                <p>
                  Approximately 2x slower than the <a href="http://www.mpfr.org" target="_top">MPFR</a>
                  or <a href="http://gmplib.org" target="_top">GMP</a> libraries.
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">mpf_float</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;</span></code>
                </p>
              </td>
<td>
                <p>
                  boost/multiprecision/gmp.hpp
                </p>
              </td>
<td>
                <p>
                  2
                </p>
              </td>
<td>
                <p>
                  <a href="http://gmplib.org" target="_top">GMP</a>
                </p>
              </td>
<td>
                <p>
                  Very fast and efficient back-end.
                </p>
              </td>
<td>
                <p>
                  Dependency on GNU licensed <a href="http://gmplib.org" target="_top">GMP</a>
                  library.
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">mpfr_float</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;</span></code>
                </p>
              </td>
<td>
                <p>
                  boost/multiprecision/mpfr.hpp
                </p>
              </td>
<td>
                <p>
                  2
                </p>
              </td>
<td>
                <p>
                  <a href="http://gmplib.org" target="_top">GMP</a> and <a href="http://www.mpfr.org" target="_top">MPFR</a>
                </p>
              </td>
<td>
                <p>
                  Very fast and efficient back-end, with its own standard library
                  implementation.
                </p>
              </td>
<td>
                <p>
                  Dependency on GNU licensed <a href="http://gmplib.org" target="_top">GMP</a>
                  and <a href="http://www.mpfr.org" target="_top">MPFR</a> libraries.
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">float128</span></code>
                </p>
              </td>
<td>
                <p>
                  boost/multiprecision/float128.hpp
                </p>
              </td>
<td>
                <p>
                  2
                </p>
              </td>
<td>
                <p>
                  Either <a href="http://gcc.gnu.org/onlinedocs/libquadmath/" target="_top">libquadmath</a>
                  or the Intel C++ Math library.
                </p>
              </td>
<td>
                <p>
                  Very fast and efficient back-end for 128-bit floating-point values
                  (113-bit mantissa, equivalent to FORTRAN's QUAD real)
                </p>
              </td>
<td>
                <p>
                  Depends on the compiler being either recent GCC or Intel C++ versions.
                </p>
              </td>
</tr>
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